KC Sinha Mathematics Solution Class 11 Chapter 29 Derications and Rules of Differentiation Exercise 29.1

 Exercise 29.1

Page no 29.9

Type 1

Question 1 

If $f(x)=x^{2}$, find $f^{\prime}(2)$

Question 2

If $f(x)=x^{3}+1$, find $f^{\prime}(3)$

Question 3

If $f(x)=x^{2}+2 x+7$, find $f^{\prime}(3)$

Question 4

If $f(x)=m x+c$, find $f^{\prime}(0)$

Question 5

If $f(t)=3 t^{2}+1$, find $f^{\prime}(1)$

Question 6

Find the derivative of $x$ at $x=1$

Question 7

Find the derivative of $f(x)=3 x$ at $x=2$

Question 8

Find the derivative of $99 x$ at $x=100$.

Question 9

Find the derivative of $x^{2}-2$ at $x=10$

Question 10

Find the derivative of $f^{\prime}(x)=3$ at $x=3$.

Question 11

Find the derivative of the constant function $f(x)=a$ for a fixed real number $a$.

Question 12

Find the derivative of $\sin x$ at $x=0$.

Question 13

If $f(x)=x^{3}+7 x^{2}+8 x-9$, find $f^{\prime}(4)$

Question 14

If $f(x)=x^{3}-2 x+1$, show that $f^{\prime}(2)=10 f^{\prime}(1)$

Question 15

If $f(x)=x^{2}-4 x+7$, show that $f^{\prime}(5)=2 f^{\prime}$

$(7 / 2)$

Question 16

Find the derivative of the function $f(x)=2 x^{2}+3 x-5$ at $x=-1$ Also prove that $f^{\prime}(0)+3 f^{\prime}(-1)=0$

Question 17

For the function $f$ given by $f(x)=k x^{2}+7 x-4, f^{\prime}(5)=97$ then find $k$

Question 18

for the function $f$ given by $f(x)=x^{2}+2 a x+5, f^{\prime}(1)=10$, find $a$

Question 19

If $f(x)=\frac{x-2}{x^{2}-3 x+2}$, when $x \neq 2$ $=1$, when $x=2$ then find $f^{\prime \prime}(2)$

Type 2

Question 20

starting at time $t=0$, a particle moves along a line so that its position after $t$ seconds is $5(t)=t^{2}-6 t+8$ meters. Find its speed at time $t=3$ seconds.

Question 21

A particle moves along a line so that at time, t its position is $s(t)=6 t-p^{2}$ What is its initial velocity ?

Question 22

A particle moves along a line so that its position at time t is $s(t)=\frac{t^{2}+2}{t+1}$ units

Find its velocity at time $t=3$.